Welcome to UNEQUAL TEMPERAMENTS!

Thank you for visiting this website, devoted
to everybody interested in Musical Temperament: performers of all Western
musical instruments, singers, keyboard tuners, instrument makers, students
and music lovers. We deal here with the very foundations of Western music: the way the different diatonic and chromatic scales arise, their acoustical foundations, their historical development, their practical use in present day performance, how to tune musical instruments and how to play them and sing in tune.

Claudio
Di Veroli, Bray,
Rep. Ireland, 2013. E-mail:

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Interested
in
Baroque interpretation for harpsichord and other keyboards?
Find
most problems resolved in the comprehensive recent book:PLAYING
THE BAROQUE HARPSICHORD

UNEQUAL TEMPERAMENTS: THEORY, HISTORY AND PRACTICE: 3rd ed.

Unequal
Temperaments, 3rd Edition, July 2013: 486 pages and 365 figures incorporating decades
of new findings in the field.

PART
ONE provides the acoustical background. Each one of the main temperaments is then
covered, with a thorough analysis of its musical features. Finally a full HISTORICAL
SURVEY guides the musician in the selection of temperament(s) for his/her repertoire.

PART
TWO consists of directions for the practice of the different unequal temperaments:
keyboard tuning procedures, fret placement in fretted strings, fingering for unfretted strings, intonation
for voices, woodwinds and brass wind instruments, including variable intonation
techniques.

PART
THREE covers multiple divisions and the analysis of historical sources,
including research results published here for the first time.

You
are welcome to read below published Reviews and
a Preview. Please click on the button below for
price details and to buy the book.

If you have purchased the UT book and wish to re-download it,
please click here
for directions.

If you purchased the UT 2nd ed. after 30th June 2012, please email us stating your name, country, Lulu Order no. and date.
Bray Baroque will send you directions for a once-only download of a free copy of the 3rd edition.

Contents
of UNEQUAL TEMPERAMENTS: THEORY, HISTORY AND PRACTICE:

PART
ONE - DESCRIPTION, ANALYSIS, HISTORY

Intervals,
Scales and Temperaments

Evaluation
method for the temperaments

Equal
Temperament and Pythagorean intonation

Just
intonations

Meantone
temperaments

Lute
temperaments

Circular
French temperaments

Circular
Good temperaments

Comparative
evaluation of temperaments

TEMPERAMENT
AND PERFORMANCE: A HISTORICAL REVIEW

PART
TWO - TUNING AND FRETTING INSTRUCTIONS

Tuning
methods and temperament schemes for keyboards

Temperament
schemes for fretted clavichords

Directions
and schemes for fretted strings

Intonation
for wind instruments, unfretted strings and voices

PART
THREE - COMPLEMENTARY TOPICS

Multiple
divisions of the octave

Analysis
of sources on temperament

Complementary
topics and Appendices

LITERATURE
CITED

Some
unique features of the UNEQUAL TEMPERAMENTS book

>
A definitive and extensive treatment of Baroque French Circular temperaments,
their evolution in theory and practice (33 pages).
> A new comprehensive analysis of the temperaments advocated
for J.S. Bach in modern times, with
exhaustive computer-aided searches for Bach's temperament, producing significant
new results (16 pages).
> A full Historical Review, with 33 sections and subsections
covering the tuning of musical scales during the successive erasin Western musical history, including differences between instruments and
countries (30 pages).
> A full treatment of Equal Temperament, its diffusion through
the Western world and evolution of tuning accuracy (12 pages).
> Charts with graphical comparisons between and within groups
of temperaments.
> Simple, accurate and fast keyboard-tuning schemes for each
temperament:both beat-rate schemes and
early-style tuning directions are included.
> Tuning schemes for fretted clavichords.
> Fretting charts for lutes and viols covering an ample assortment of temperaments and
open-string tunings.
>
Full charts and directions for unequal temperament fingering for violins
and other unfretted strings.
> Charts and directions for unequal temperaments in early woodwinds.
> The most complete ever treatment of unequal temperaments for
natural brass instruments.
> Different methods for improved intonation in Equal Temperament are also included.> New improved spreadsheet and other extras downloadable from
our Unequal Temperament goodies webpage .

Why an
eBook?

This book can be read
on the screen of a PC, Mac and any desktop or portable device capable
of showing PDF documents (Adobe Acrobat v.6.0 or later). It is also
formatted for impeccable printing on Letter, A4 or A5 (two pages
in an A4 sheet) paper. Benefits of buying an eBook compared to a ready-printed
volume: 
PRICE: less than 1/5th of the estimated price of a printed
volume. (*) 
AVAILABILITY: an eBook is never out of print. 
SECURITY: the reader can make a backup copy, so that the eBook
cannot be lost or stolen. 
PRINTING: if a printed volume is really needed, the reader
can print it from any home computer. 
MANYFIGURES: hundreds of figures, including many full-colour
photos and charts. 
COLOUR: colour is freely used in the text and tables, helping
to easily understand complex matters and relationships. PORTABILITY: the reader can carry the book around in a laptop computer,
smartphone or any other portable device. KINDLE etc.: the text is fully readable. The PDF does not resize fonts: you just zoom-in to see details or enlarge text.
You can also convert the PDF into a mobi (Kindle) file or some other format using one of the free utilities available online (such as Calibre). 
REFERENCE:
the reader interested in a particular topic can quickly search and find
all the references to it in the eBook. 
TIMELINESS:
you buy the eBook, download it immediately and can begin reading it straight
away. 
WEB ADDRESSES: they allow easy access to the web pages referred to.(**)

(*) There are no plans to make this book available in printed form. The eBook is a 20+Mb document file that downloads in less than two minutes using a typical Internet broadband service.

(**) On p. 14 of the 3rd edition, the 6th bullet reads: "HYPERLINKS. They are no longer included in this edition: most of them failed to work in the final PDF file, a common issue of the conversion of large files. ... the reader can just copy any web address from the text and paste it into the address box of the web browser." Nevertheless, the final conversion to PDF has reconverted all the "http://... " addresses into hyperlinks and they are all working now: just clicking on the link opens the web page in the user's Internet browser.

Published
Book Reviews

David
Hitchin in The British Clavichord Society newsletter, No.45, Oct.2009:

"Claudio
Di Veroli's work has the advantage (or disadvantage) of being at least
twice the size of those by his competitors. In the eleven chapters of the first part
Di Veroli introduces musical intervals, the Pythagorean scale, equal temperament,
just intonations, meantone, ... lute temperaments, irregular French and
irregular 'good' temperaments, comparative evaluations and a review of
historic performance. He defines a series of seventeen principles ...
They provide a solid framework for understanding and comparing temperaments.
The author occasionally uses measures likely to be known only to those
with an advanced statistical training (he was a student of Sir David Cox,
one of the most eminent British statisticians). As a statistician myself,
I can confirm that his choice of methods is appropriate ... The
second part is about tuning and fretting instructions ... There is advice
about hearing and using beats, thirty hints and tricks for harpsichord
tuning, transposing instruments ... a list of schemes for keyboard instruments,
fretting instructions for lutes and viols, intonation for violins and
voices, woodwinds and brass instruments.The
third part ... includ[es] multiple divisions ... and an analysis of much
of the historic documentation for temperaments. The
book contains some original research. Di Veroli concludes that Barnes'
temperament is the optimum one for the Well-Tempered Clavier ...
Di Veroli generated and evaluated the nearly 17 million possibilities,
and found that very slight improvements were possible, but they were so
small, and made tuning so much more difficult, that they were not worth
using in preference to Barnes.
... many pages make good use of colour ...
Di Veroli ... includes links to audio files, and surely there is nothing
more self-evident than the need to hear different temperaments as one
reads about them ... There are also two useful spreadsheets. ... This
work is only available as ... a .pdf file ... I printed it out. It is
formatted for convenient printing on A4 paper, but it was quite legible
when reduced to A5 ... a pleasure to read ... the explanations
are clear and easy to follow. He has taken on a Herculean task of reviewing
and explaining the history and application of unequal temperaments, and
while it is unlikely that all experts in the subject will agree with him
on all points, he presents convincing arguments and detailed documentation.
... This is one of the most interesting books that I have read for a long
time."

Please
click here
for details about a most unusual review, as well as a published rebuttal.

Pedro
Persone in Early Music
America, Spring 2010, Mar.2010:

"This
e-book, published in March 2009, is now available on-line ... Di Verolis
study is divided into three main parts. Part I consists of Description,
Analysis and History (11 chapters in total). The seven chapters
of Part II explain Tuning and Fretting Instructions. Part
III consists of Complementary Topics (four chapters and five
appendices). Di Veroli´s book is a relevant complementary source
to the existing bibliography on the important subject of temperament and
can be counted among the best-known books in the field. ...
...it is ... necessary to temper our instruments
... the difference ... is the "dust" we have to sweep under
the rug. Di Veroli provides us with the recipes on how to distribute our
"dust" by using the historical unequal temperaments. He does
this by means of symbols, ratios and formulas, and explanations ... The
most important temperaments are explained in this book ... In
addition, Di Veroli ... offers important tips about the way to manage
tuning hammers or how to change a keyboard temperament shortly before
a public performance. The huge number of known temperaments are explained
step by step, and fretted clavichords are given a separate chapter. The
e-book also offers information about plucked fretted instruments and the
intonation of woodwind and brass instruments.
I am very happy to recommend this book,
since it will provide pleasant and useful reading for both students and
enthusiasts."

Comments by Readers and Scholars: Ever since 2009 the author has received
many personal comments from readers, happy with the book's
structure, coverage, presentation and cost. As for the 3rd edition of 2013, the temperament specialist Fred Sturm has recommended it in the online forum of the Piano Technicians Guild, stating that: "It is the most comprehensive and reliable source for information about temperament history available today".The world-leading temperament scholar Prof. Patrizio Barbieri (author of the "Enharmonic Instruments and music" treatise) has written to the authorwith permission to publishthat Unequal Temperaments in its 3rd ed. is most likely to be the best treatise in the field.

Excerpts
from UNEQUAL TEMPERAMENTS

1978 ... the book Unequal Temperaments and their Role in the Performance of Early Music ... Rudolf Rasch published ... a detailed review
in Stimulus ... Rasch praised both the theoretical framework
and the emphasis in the historical relevance of each temperament
for present-day performance ...
Quite a few musicians wrote
... positive comments ... Let me just mention ... Igor Kipnis
Hubert Bédard and John Barnes . Bédard
wrote: 'The most useful text on the subject I have seen yet.
This book seems to settle the matter at last.'. ...

Three decades having elapsed ... in 2007 I started working on this new book ... not a revision but a new treatise written from scratch
... it incorporates the results of new published research, including recent discussions by/with colleagues. ... Readers of the 3rd. edition will find significant additions or enhancements ...

With our
simple yet powerful "dissection tools", we are now ready
to enter, in the following Chapters, the fascinating world of early
temperaments in Renaissance, Baroque and Classical times. ... In meantone
temperament contrary to an often repeated but erroneous belief,
the main restriction to further modulations is not caused
by the wolf fifth, but instead by the 4 wolf major thirds
...

The fascinating
properties and proportions of the Standard meantone diatonic and
chromatic scales are treated in the next Chapter ...Let us
now see how ancient musicians, and their modern followers, fare
in practice when they need a Spiral of Fifths with up to 5 pairs
of flats and sharps ... : Voices, unfretted strings, trombones and
trombe da tirarsi ... Other brass wind instruments ... Fretted strings
...Woodwinds ... Keyboards ...

... Chaumont and F.Couperin were
using different variants ... The reconstructed Couperin organ temperament
is shown below. ...

A disproportionate
amount of effort and ink has been dedicated [by modern writers]
to the analysis of the multiple variants of circular temperaments
proposed by German Baroque theoreticians. ... We will eventually
conclude that only a handful of these systems are really worth studying
and tuning to. ... If
the reader finds it difficult to grasp which flavour of 'Good'
temperament J.S.Bach advocated or preferred, he/she is in good company.
...

Bach did not
compose the WTC in order to advocate a peculiar tuning to be discovered
by archaeologists of the future deciphering 'Rosetta stones'.
A full classification
... (Artusi 1603) had the instruments divided into three
families according to their temperament However as
we come into the Baroque era, fretted instruments are found increasingly
playing together with keyboards

The Baroque
is the only period in Western musical history in which the different
amount of temperament of the intervals around the Circle of Fifths
eventually became a component of musical expression.
During the Classical period, unequal
temperaments were still feasible and practised throughout Europe.
But Equal Temperament was now gaining considerable momentum.
What was the most common situation in the so-called Classical
period? What were most musicians doing after 1750?

THIRTY(30) HINTS
AND TRICKS FOR HARPSICHORD TUNING. [For] early stringed keyboards
the following guidelines are an integrated set of suggestions
and instructions in a working-practice sequence. ...MEANTONE FRETTING. Unlike the pure intonations where some considerable
mistuning was expected by early audiences and anyway unavoidable
in meantone an accurate tuning is both feasible and
expected. A simple [fretting] procedure follows

Standard French
ordinaire being the most unequal circular temperament, the
conclusion back in 1978 was that a most accurate fretting was possible
for all the remaining circular temperaments as well. This has now
been confirmed after three decades of success
This Chapter
is intended to show how to play easily and accuratelyunfretted
instruments in unequal temperaments. This is achieved by using specific
fingering charts and techniques. ... The text has been written so
as to be most useful to singers as well.

The road
to intonation hell is paved with just-intonation intentions.
... Were Bach's
horn and trumpet players (for example the famous Reiche) better
than Handel's (for example the famous Snow)? ... were perhaps Bach's
players using narrow-bore instruments with increased flexibility and ease in the upper parts of the
register?

Now
that you bought the UT book, enjoy the Sound Examples, Spreadsheet and
other extras

The Unequal
Temperaments: Theory, History and Practice eBook is a self-contained
work. No additional files are needed to read it, understand it, enjoy
it and/or put the advice into practice. Once you have purchased the book,
however, additional goodies are waiting for you to enhance your experience:
an updated Errata and Addenda file, the new Unequal Temperament Spreadsheet and a full set of Sound Examples. You can access them
from the Unequal Temperament Goodies webpage.

Please find in
a separate webpage, Unequal Temperament Links, links to other sites with contents we find interesting and useful.

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